Traditional methods for detecting genes that affect complex diseases in humans or animal models, milk production in livestock, or other traits of interest, have asked whether variation in genotype produces a change in that trait’s average value. But focusing on differences in the mean ignores differences in variability about that mean. The robustness, or uniformity, of an individual’s character is not only of great practical importance in medical genetics and food production but is also of scienti?c and evolutionary interest (e.g., blood pressure in animal models of heart disease, litter size in pigs, ?owering time in plants). We describe a method for detecting major genes controlling the phenotypic variance, referring to these as vQTL. Our method uses a double generalized linear model with linear predictors based on probabilities of line origin. We evaluate our method on simulated F2 and collaborative cross data, and on a real F2 intercross, demonstrating its accuracy and robustness to the presence of ordinary mean-controlling QTL. We also illustrate the connection between vQTL and QTL involved in epistasis, explaining how these concepts overlap. Our method can be applied to a wide range of commonly used experimental crosses and may be extended to genetic association more generally.

As the molecular marker density grows, there is a strong need in both genome-wide association studies and genomic selection to fit models with a large number of parameters. Here we present a computationally efficient generalized ridge regression (RR) algorithmfor situations where the number of parameters largely exceeds the number of observations. The computationally demanding parts of the method depend mainly on the number ofobservations and not the number of parameters. The algorithm was implemented in the R package bigRR based on the previously developed package hglm. Using such an approach, a heteroscedastic effects model (HEM) was also developed, implemented and tested. Theefficiency for different data sizes were evaluated via simulation. The method was tested for a bacteria-hypersensitive trait in a publicly available Arabidopsis dataset including 84 inbred lines and 216 130 SNPs. The computation of all the SNP effects required less than10 seconds using a single 2.7 GHz core. The advantage in run-time makes permutationtest feasible for such a whole-genome model, so that a genome-wide significance threshold can be obtained. HEM was found to be more robust than ordinary RR (a.k.a. SNPBLUP) in terms of QTL mapping, because SNP specific shrinkage was applied instead of acommon shrinkage. The proposed algorithm was also assessed for genomic evaluation and was shown to give better predictions than ordinary RR.